PYQ NEET- Mechanical Properties Of Fluids L-2

Question: The velocity of a small ball of mass $M$ and density $d$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $d / 2$, then the viscous force acting on the ball will be#

[NEET 2021]

A) $\frac{M g}{2}$

B) $M g$

C) $\frac{3}{2} M g$

D) $2 \mathrm{Mg}$

Answer: $\frac{M g}{2}$#

Sol:#

Given, the density of the small ball is $d$

The mass of the small ball is $M$

The density of the glycerine is $d / 2$.

As we know that,

viscous force $=$ weight - buoyant force

Viscous force $=V d_1 g-V d_2 g$

Here, $V$ is the volume of submerged bodies,

$g$ is the acceleration due to gravity,

$d_1$ is the density of the small ball,

$d_2$ is the density of the glycerine,

$$ d_1=d \text { and } d_2=d / 2 $$

Substituting the given values in the viscous force expression, we get

Viscous force $=V d g-V \frac{d}{2} g$

Viscous force $=\frac{V d g}{2}=\frac{M g}{2} \quad(\because M=d \times V)$